### Center Path

Four rods of equal length are hinged at their endpoints to form a rhombus. The diagonals meet at X. One edge is fixed, the opposite edge is allowed to move in the plane. Describe the locus of the point X and prove your assertion.

### Tied Up

In a right angled triangular field, three animals are tethered to posts at the midpoint of each side. Each rope is just long enough to allow the animal to reach two adjacent vertices. Only one animal can reach all points in the field. Which one is it and why?

### The Cyclic Quadrilateral

This gives a short summary of the properties and theorems of cyclic quadrilaterals and links to some practical examples to be found elsewhere on the site.

# Right Angles

##### Stage: 3 Challenge Level:

Can you make a right-angled triangle on this peg-board by joining up three points round the edge?
Can you work systematically to prove this?

Full Screen Version
If you can see this message Flash may not be working in your browser
Please see http://nrich.maths.org/techhelp/#flash to enable it.

Now try changing the number of points round the edge.
Can you do it now?

Can you show by calculation that the angle is a right angle?
What do you notice about the side of the triangle opposite the right angle?

Try this with other numbers of points round the edge.
When is it possible to make a right-angled triangle?

In this interactivity, the points are equally spaced around a circle. Imagine that they are not.
Can you explain the conditions which will give a right-angled triangle?
Can you prove this?

For printable sets of circle templates for use with this activity, please see Printable Resources page.

Many thanks to Geoff Faux who introduced us to the merits of the 9 pin circular geo-board.
The boards, moulded in crystal clear ABS that can be used on an OHP (185 cm in diameter), together with a teacher's guide, are available from Geoff at Education Initiatives